This discussion will first explain how a simple synchronous motor operates, and then explain one type of prior-art speed control used with such a motor.
Synchronous Motor
FIG. 1 illustrates schematically three stator coils 3, 6, and 9, which are contained in a three-phase synchronous motor (not shown). FIG. 2 shows the coils, but with connecting wires W of FIG. 1 omitted, to avoid clutter. In FIG. 2, currents 13, 16, and 19 are generated in the respective coils. Each current produces a magnetic field B3, B6, and B9, as indicated.
The coils 3, 6, and 9 are physically positioned to be 120 degrees apart, as shown, so that the fields B3, B6, and B9 are also positioned 120 spatial degrees apart. This arrangement allows creation of a magnetic field which rotates in space at a constant speed, if proper currents are generated in the coils, as will now be explained.
FIG. 3 illustrates three-phase currents. The vertical axis on the coordinates runs from negative unity to positive unity for simplicity. In practice, one would multiply the values of unity by the actual peak-to-peak values of the currents being used.
Currents in the form of sine waves SIN3, SIN6, and SIN9 are created respectively in coils 3, 6, and 9, as indicated. Coil 3 resides at zero physical degrees. SIN3 begins at zero electrical degrees, as indicated on the plot.
Similarly, coil 6 stands at 120 degrees from coil 3. SIN6 begins at 120 degrees, as indicated on the plot. Similarly, coil 9 stands at 240 degrees from coil 3. Correspondingly, SIN9 begins at 240 degrees, as indicated on the plot.
Each coil 3, 6, and 9 produces a magnetic field, as indicated. Those three magnetic fields add vectorially to produce a single magnetic field. Two examples will illustrate this vectorial addition.
In the first example, time T1 is chosen in FIG. 3, which corresponds to 255 electrical degrees. T1 is also indicated in FIG. 4. At this time T1, the values of the currents I3, I6, and I9 are indicated. Those currents exist in coils 3, 6, and 9 in FIGS. 2 and 3. Those currents produce magnetic fields which are roughly proportional to the currents.
Since the coils 3, 6, and 9 are physically positioned at angles of zero, 120, and 240 degrees, the magnetic fields are also positioned at those angles. The magnetic fields are indicated as B3, B6, and B9 in FIG. 4.
It is noted that field B3 is positioned at 180 degrees, rather than zero degrees. This occurs because current 13 is negative, thus producing a magnetic field B3 which is 180 degrees from the magnetic field which would be produced by a positive current.
Field-vectors B3, B6, and B9 are re-positioned within circle C1, to show vector addition. They sum to the resultant vector R1. Resultant R1 represents the vector sum of the three magnetic fields, and is an actual magnetic field vector located in space. Resultant R1 is the magnetic field produced by the three coils, and is termed the stator field.
In the second example, time T2 in FIG. 3 is chosen, which corresponds to 330 electrical degrees. T2 is also indicated in FIG. 5. At this time T2, the particular values of currents I3, I6, and I9 are indicated.
It is noted that I3 and I6 are superimposed over each other: the same arrow represents both. It should be observed that these two identical currents produce two magnetic fields of the same size at this time. However, because the two currents I3 and I6 are applied to coils which are physically 120 degrees apart, the magnetic fields are oriented differently in space.
The magnetic field vectors produced are indicated as B3, B6, and B9 in FIG. 5.
It is noted that fields B3 and B6 are positioned at 180 and 300 degrees, respectively, rather than at zero and 120 degrees. As before, this occurs because currents I3 and I6 are negative, producing magnetic fields B3 and B6 which are 180 degrees rotated from the magnetic field which would be produced by positive voltages.
Field-vectors B3, B6, and B9 are re-positioned within circle C2, to show vector addition. They sum to the resultant vector R2. Resultant R2 represents the vector sum of the three magnetic fields, and is an actual magnetic field vector located in space. It is the stator field.
If these two examples are repeated for every angle from zero to 360 in FIG. 3, it will be found that a resultant R in FIG. 6 is produced at each angle, and that all resultants R are identical in length. It will also be found that, as one computes resultant R for sequential angles, that resultant R rotates at a uniform speed around circle C.
The arrangement just described produces a constant magnetic field which rotates at a constant speed. This rotating field can be used as shown in FIG. 7.
FIG. 7 illustrates the coils of FIG. 2. A rotor ROT is added, which contains a rotor magnetic field RF, produced by a magnetic field source FS, which may be a permanent magnet or electrical coil. Because of the laws of physics, the rotor field RF will attempt to follow the rotating resultant R. Consequently, the rotating resultant R induces rotation in the rotor ROT, producing motor-action.
Control System
A prior-art approach to controlling speed of the motor just described will be given. In one approach, the basic idea is to maintain the resultant stator field R in FIG. 7 at 90 degrees ahead of the rotor field RF. (FIG. 7 shows the resultant R at zero degrees with respect to RF.)
The particular approach to be explained is sometimes termed “Field Oriented Control,” FOC. In FOC, the stator field is transformed, or superimposed, onto a rotating coordinate system, and is then compared with the rotor field, within the rotating coordinate system. Under this approach, two fields (stator and rotor) are, ideally, not changing with respect to each other and, when they do change, they change slowly, with respect to each other. FOC reduces bandwidth requirements, especially in Proportional Integral controllers, used to control the error between the two fields.
Perhaps an analogy can explain the bandwidth reduction. Assume two race horses traveling on a circular track. Each, in essence, can be represented by a hand on a clock. In one approach, a stationary observer can, say, every second, compute position of each horse, compare the positions, and deduce a difference between positions. In essence, the observer computes an angle for each hand of the clock, and continually compares those changing angles. However, even if the horses are running nose-to-nose, the observer still must compute an angle for each horse every second, and each angle changes, second-to-second.
In the FOC approach, the observer, in essence, rides along with the horses. If the horses are nose-to-nose, the observer computes a steady zero difference. When one horse passes the other, the observer computes a slowly changing difference.
The FOC approach reduces the number of a certain type of computation which must be done, thereby reducing bandwidth requirements.
In explaining FOC, a current in a coil will sometimes be treated interchangeably with the magnetic field which the coil produces. One reason is that the two parameters are approximately proportional to each other, unless the coil is saturated. Thus, a current and the field it produces differ only by a constant of proportionality.
FIG. 8 is a schematic of the connection of the three coils C3, C6, and C9 in one type of synchronous motor (not shown). They are connected in a WYE configuration, with point PN representing neutral.
A significant feature of the WYE configuration is that the currents in the coils are not mutually independent. Instead, by virtue of Kirchoffs Current Law, the three currents must sum to zero at point PN. Thus, only two independent currents are present, because once they are specified, the third is thereby determined. One significance of this feature will be explained later, in connection with the present invention.
A CONTROLLER 50 measures and controls the currents I3, I6, and I9, in a manner to be described. It is again emphasized that each current I3, I6, and I9 produces a respective magnetic field B3, B6, and B9 which are separated in space by 120 degrees, as indicated. (B3, B6, and B9 in FIG. 8 only show the different directions in space, but not different magnitudes.)
The CONTROLLER 50 undertakes the processes which will be explained with reference to FIGS. 9–14. Block 55 in FIG. 9 indicates that the CONTROLLER 50 in FIG. 8, or an associated device, measures each current I3, I6, and I9. In block 57 in FIG. 9, a data point, or vector, for each current is computed, giving the magnitude and direction of the magnetic field produced by each current. For example, if the measurement occurred at time T1 in FIG. 4, then vectors B3, B6, and B9 would be computed. Those vectors are shown adjacent block 57 in FIG. 9.
In block 60, two orthogonal vectors are computed which produce the equivalent magnetic field to the resultant of the vectors computed in block 57. The two graphs adjacent block 60 illustrate the concept. STATOR FIELD is the vector sum of the three vectors B3, B6, and B9 which were previously computed in block 57. Two orthogonal vectors a and b are now computed, which are equivalent to that vector sum, namely, the STATOR FIELD. Parameter a is the length of a vector parallel with the x-axis. Parameter b is the length of a vector parallel with the y-axis.
FIG. 10 illustrates how this computation is performed, and is presented to illustrate one complexity in the prior art which the present invention eliminates, or reduces. FIG. 10 illustrates three generalized vectors I1, I2, and I3, which are illustrated across the top of FIG. 10. The overall procedure is to (1) compute the x- and y-coordinates for each vector, (2) add the x-coordinates together, and (3) add the y-coordinates together. The result is two orthogonal vectors.
As to the x-coordinates, as indicated at the top center of FIG. 10, the x-coordinate of I2 is I2(COS 120). As indicated at the top right, the x-coordinate of I3 is I3(COS 240). As indicated at the top left, the x-coordinate of I1 is I1(COS 180). These three x-coordinates are added at the lower left, producing a vector Ia.
As to the y-coordinates, as indicated at the top center of FIG. 10, the y-coordinate of I2 is I2(SIN 120). As indicated at the top right, the y-coordinate of I3 is I3(SIN 240). There is no y-coordinate for I1, because it always stands at either zero or 180 degrees. These y-coordinates are added at the lower right, producing a vector Ib.
FIG. 11 shows the two vectors Ia and Ib. Their vector sum is the STATOR FIELD, as indicated. These two vectors Ia and Ib correspond to the two vectors computed in block 60 in FIG. 9.
In block 70 in FIG. 12, rotor angle, theta, is measured. A shaft encoder (not shown) is commonly used for this task. Rotor angle is an angle which indicates the rotor field vector, either directly or through computation.
In block 80, the two vectors computed in block 60 in FIG. 9 are transformed into a coordinate system which rotates with the rotor. (The angle theta is continually changing.) The graphs adjacent block 80 illustrate the concept. The STATOR FIELD, as computed in block 60 in FIG. 9, is on the left, and has x-y coordinates of (a,b). Block 80 transforms the coordinates to a1 and b1, shown on the right, which are the coordinates for the same STATOR FIELD, but now in a rotating u-v coordinate system.
FIG. 13 illustrates how this transformation may be accomplished. Plot 100 illustrates a generalized point P, representing a generalized stator field vector, having coordinates (a, b) in an x-y coordinate system. Plot 105 illustrates how the u-coordinate, of value a1, can be computed for a rotated u-v coordinate system. Plot 110 illustrates how the v-coordinate, of value b1, can be computed for the rotated u-v coordinate system. Equations 115 summarize the results.
Parameters a1 and b1 are the variables computed by block 80 in FIG. 12. It is noted that coordinate b1 corresponds to a vector which is parallel to the LEADING ORTHOGONAL in the graph adjacent block 90. The significance of this will become clear shortly.
Block 90 in FIG. 12 computes the error, if any, between the STATOR FIELD (shown adjacent block 80) and the LEADING ORTHOGONAL in the plot adjacent block 90. The LEADING ORTHOGONAL is a vector which is perpendicular to the ROTOR FIELD, and leads the ROTOR field. In order to maximize torque, the stator field is controlled so that it continually remains aligned parallel with the LEADING ORTHOGONAL, also called the quadrature vector to the ROTOR FIELD. (In generator action, as opposed to motor action, the quadrature vector lags the ROTOR FIELD.) This evaluation is done in the rotating coordinate system u-v, as block 90 indicates.
Block 130 in FIG. 14 indicates that the vector coordinates of the required stator field are computed, but in the rotating coordinate system. The graph adjacent block 130 illustrates the concept. The NEEDED FIELD is that which is orthogonal with the ROTOR FIELD. In the graph, the STATOR FIELD illustrated is not orthogonal, and corrective action must be taken.
The coordinates computed in block 130 for the required stator field lie in the rotating u-v coordinate system. Block 135 transforms those coordinates into the stationary x-y coordinate system, using inverses of the operations shown in FIG. 13. The inverse operations arex=u COS (theta)−v SIN (theta)y=u SIN (theta)+v COS (theta)
Block 140 in FIG. 14 then computes the required voltages needed for the coils to attain the required stator field. In concept, block 135 specifies a vector analogous to resultant R1 in FIG. 4. Block 140 in FIG. 14 computes the voltages analogous to V3, V6, and V9 required to produce that vector R1.
The computation of block 140 is of the same type as that shown in FIG. 10. In the latter, two orthogonal vectors are derived which are equivalent to three vectors. In block 140, three vectors are derived from two orthogonal vectors.
Then the processes of FIGS. 9–14 are continually repeated during operation of the motor.
The preceding was a simplification. In practice, various prior art control strategies are used in the process of converging the stator field to the required stator field, that is, in reducing the error of block 90 to zero, by adjusting the currents in the coils. These control strategies were not discussed.
The Inventors have developed a less expensive approach to controlling a synchronous motor.